[tex]\pi[/tex]
Explanation
The distance between the repetition of any function is called the period of the function( this is not the graph of the function, it is another periodic function)
therefore, to find the period, find the distance between 2 identical values for y, so
[tex]\text{period}=X_2-X_1[/tex]
so
[tex]\text{period}=X_2-X_1[/tex]
so, let
[tex]\begin{gathered} X_2=\frac{\pi}{2} \\ X_1=-\frac{\pi}{2} \end{gathered}[/tex]
hence
[tex]\begin{gathered} \text{period}=X_2-X_1 \\ \text{period}=\frac{\pi}{2}-(-\frac{\pi}{2})=\frac{\pi}{2}+\frac{\pi}{2}=\pi \end{gathered}[/tex]
therefore, the answer is:
[tex]\pi[/tex]
I hope this helps you
